Drawing from the book
Basics of Error Control Codes
Drawing from the book
Information Theory, Inference, and Learning Algorithms
David MacKay
? Cambridge Univ. Press 2003
Downloadable or purchasable:
CSE 466
Error Correcting Codes
1
Channel coding aka Forward Error Correction
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¡°My communication system is working, but I am getting a lot of errors¡what
can I do?¡±
CRC is an error DETECTING code¡it spots errors with high probability, but
doesn¡¯t tell you how to fix them
Error CORRECTING codes can actually allow you to repair the errors¡if
there aren¡¯t too many
CSE 466
Error Correcting Codes
2
The big picture
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Channel coding is adding redundancy to improve reliability, at a cost in rate
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Source coding is removal of redundancy from information bits to improve rate
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Error correction
Compression
This lecture is only about channel coding
CSE 466
Error Correcting Codes
David MacKay
Information Theory, Inference, and Learning
Algorithms
? Cambridge Univ. Press 2003
3
How do error correcting codes work?
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Basic idea: add redundancy (extra bits) to make
communication more robust
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Or, put another way, don¡¯t allow all bit patterns, just a subset¡if
you receive an invalid bit sequence, correct to the closest valid bit
sequence
The extra bits (or disallowed bit patterns) reduce the net
communication rate:
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CSE 466
If ¡°information bits¡± are denoted i and ¡°error correction bits¡±
denoted ec, then the new rate, with error correction is i/(i+ec)
The original rate, with no error correction (ec=0) is 1.0
Error Correcting Codes
4
Noisy communication channels
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EF modem
modem
wifi card
Galileo probe
Parent cell
RAM
RAM
printer
CSE 466
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airgap
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phone line ?
radio waves ?
radio waves ?
daughter cell 1
daughter cell 2
disk drive
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flash memory?
QR code
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Error Correcting Codes
EF modem
modem
wifi card
Earth
RAM
RAM
phone camera
5
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